CERN-EP-2018-161 2018/12/24
CMS-SMP-17-005
Measurement of differential cross sections for Z boson pair
production in association with jets at
√
s
=
8 and 13 TeV
The CMS Collaboration
∗Abstract
This Letter reports measurements of differential cross sections for the production of
two Z bosons in association with jets in proton-proton collisions at √s = 8 and
13 TeV. The analysis is based on data samples collected at the LHC with the CMS
detector, corresponding to integrated luminosities of 19.7 and 35.9 fb−1 at 8 and
13 TeV, respectively. The measurements are performed in the leptonic decay modes
ZZ → `+`−`0+`0−, where `,`0 = e, µ. The differential cross sections as a function
of the jet multiplicity, the transverse momentum pT, and pseudorapidity of the pT
-leading and sub-leading jets are presented. In addition, the differential cross sections as a function of variables sensitive to the vector boson scattering, such as the invariant
mass of the two pT-leading jets and their pseudorapidity separation, are reported. The
results are compared to theoretical predictions and found in good agreement within the theoretical and experimental uncertainties.
Published in Physics Letters B as doi:10.1016/j.physletb.2018.11.007.
c
2018 CERN for the benefit of the CMS Collaboration. CC-BY-4.0 license ∗See Appendix A for the list of collaboration members
1
Introduction
The production of massive vector boson pairs is a key process for the understanding of both the non-Abelian gauge structure of the standard model (SM) and of the electroweak symmetry breaking mechanism. Thus, relevant information can be gathered measuring vector boson scat-tering [1] and triboson production processes that occur through the electroweak (EW) produc-tion of jets in associaproduc-tion with bosons. Because of the very low cross secproduc-tions for these processes compared to others leading to the same final state, a detailed understanding of the quantum chromodynamics (QCD) corrections to the associated production of vector boson pairs and jets is of paramount importance. The analysis presented in this Letter has been designed to provide such detailed understanding.
Both the ATLAS and CMS Collaborations have measured the inclusive production cross section of Z boson pairs and the differential cross sections as a function of Z boson pair observables [2– 8]. In this Letter we present new measurements of differential cross sections for the production
of two Z bosons in association with jets in proton-proton (pp) collisions at√s = 8 and 13 TeV
that extend the analyses of Refs. [6, 8] to jet variables. The most recent publication from the AT-LAS Collaboration [4] includes jet variables as well. The decay modes of the Z boson to electron
and muon (` = e, µ) pairs have been exploited. Reconstructed distributions are corrected for
event selection efficiency and detector resolution effects by means of an iterative unfolding technique, which makes use of a response matrix to map physics variables at generator level onto their reconstructed values.
This Letter presents the dependence of the cross section on the jet multiplicity and the kinematic
properties of the two pT-leading jets (where pTis the transverse momentum). Comparison with
theoretical predictions provides an important test of the QCD corrections to ZZ production.
Normalized differential cross sections as a function of the pT and pseudorapidity η of the two
pT-leading jets, as well as their invariant mass (mjj) and pseudorapidity separation (∆ηjj), are
presented. The study of mjjestablishes the basis for future multiboson final-state searches and
for the investigation of phenomena involving interactions with four bosons at a single vertex,
while the measurement of the ∆ηjj distribution is instrumental in the study of vector boson
scattering. The analysis presented in this paper together with the analyses reported in [5–9] seeks a detailed understanding of the SM processes that generate four leptons in the final state through the production of two Z bosons. All measurements are compared to predictions from recent Monte Carlo (MC) event generators. The data sets correspond to integrated luminosities
of 19.7 and 35.9 fb−1, collected by the CMS Collaboration at 8 and 13 TeV, respectively.
2
The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diame-ter, providing a magnetic field of 3.8 T. Within the solenoid volume are silicon pixel and strip tracking detectors, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the η coverage provided by the barrel and endcap detectors up
to|η| =5. Muons are measured in gas-ionization detectors embedded in the steel flux-return
yoke outside the solenoid, using three different technologies: drift tubes for|η| <1.2, cathode
strip chambers for 0.9 < |η| < 2.4, and resistive plate chambers for |η| < 1.6. The silicon
tracker measures charged particles within the range|η| <2.5. For nonisolated particles in the
range 1< pT < 10 GeV and|η| <1.4, the track resolutions are typically 1.5% in pTand 25–90
The first level of the CMS trigger system [11], composed of custom hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events within a time interval of less than 4 µs. The high-level trigger processor farm further decreases the event rate from around 100 kHz to less than 1 kHz, before data storage.
A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [12].
3
Signal and background simulation
Several MC event generators are used to simulate the signal and background contributions. The MC simulation samples are employed to optimize the event selection, evaluate the signal efficiency and acceptance, estimate part of the background, and extract the unfolding response matrices used to correct for detector effects in the measured distributions.
For the 8 TeV data analysis, MADGRAPH5 1.3.3 [13, 14] is used to simulate the production
of the four-lepton final state at leading order (LO) in QCD with up to 2 jets included in the
matrix-element calculations.POWHEG2.0 [15–18] is used for the simulation of the same process
at next-to-leading-order (NLO). A sample of events generated with MADGRAPH5 aMC@NLO
2.3.3 (abbreviated as MG5 aMC@NLOin the following) [14, 19], which simulates signal
pro-cesses at NLO with zero and one jet included in the matrix-element calculations, is produced only at generator level and used for comparison purposes. For the 13 TeV data analysis, the four-lepton processes are simulated at NLO in QCD with 0 or 1 jet included in the
matrix-element calculations with MG5 aMC@NLOand withPOWHEG2.0 at NLO. The latter is scaled
by a factor of 1.1 to reproduce the total ZZ production cross section calculated at
next-to-next-to-leading order (NNLO) [20] at 13 TeV. MG5 aMC@NLOandPOWHEG2.0, for both the 8 and
13 TeV analyses, include ZZ, Zγ∗, Z, and γ∗γ∗ processes, with the generator level constraint
m`+`− >4 GeV applied to all pairs of oppositely charged same-flavor leptons, to avoid infrared
divergences.
The gg → ZZ processes, which occur via loop-induced diagrams, are generated at LO with
MCFM 6.7 (7.0) [21] for the 8 (13) TeV analysis. The 13 TeV samples are scaled by a factor of
1.7 to match the cross section computed at NLO [22]. Electroweak production of four leptons
and two jets is simulated at LO with PHANTOM[23]. This sample includes triboson processes,
where the Z boson pair is accompanied by a third vector boson that decays into jets, as well as diagrams with quartic vertices.
Other diboson and triboson processes (WZ, Zγ, WWZ) as well as ttZ, tt, and Z+jets samples are
generated at LO with MADGRAPH5 for the 8 TeV analysis, and at NLO with MG5 aMC@NLO,
for the 13 TeV analysis.
For the 8 TeV analysis, thePYTHIA6.4.24 [24] package, with parameters set by the Z2* tune [25],
is used for parton showering, hadronization, and the underlying event simulation for all MC
samples except for MG5 aMC@NLO, for whichPYTHIA8.205 [26] is employed. The default sets
of parton distribution functions (PDFs) are CTEQ6L [27] for the LO generators, and CT10 [28],
for the NLO ones. For the 13 TeV analysis, PYTHIA 8.212 [26], with parameters set by the
CUETP8M1 tune [29], is used for parton showering, hadronization, and the underlying event simulation. The NNPDF3.0 [30] PDF set is the default. For all simulated event samples, the PDFs used are evaluated at the same order in QCD as the process in the sample.
The detector response is simulated using a detailed description of the CMS detector
algorithms used for the data. The simulated samples include additional interactions per bunch crossing, referred to as pileup. Simulated events are weighted so that the pileup distribution reproduces that observed in the data, with an average of about 21 (27) interactions per bunch crossing for the 8 (13) TeV data set.
4
Particle reconstruction and event selection
The primary triggers for this analysis require the presence of two loosely isolated leptons of the
same or of different flavor. The minimum pTfor the first lepton is 17 GeV, while it is 8 (12) GeV
for the second lepton in the 8 (13) TeV analysis. Triggers requiring a triplet of low-pT leptons
with no isolation requirement and, for the 13 TeV analysis, isolated electron and
single-muon triggers, with minimal pT-thresholds of 27 and 22 GeV, respectively, help to increase the
efficiency. The overall trigger efficiency for events that pass the ZZ selection is greater than 98%.
The offline event selection procedure is similar to that of the inclusive ZZ analyses [6–8] and is based on a global event description [32] that classifies particles into mutually exclusive cate-gories: charged hadrons, neutral hadrons, photons, muons, and electrons. Events are required to have at least one vertex [10] within 24 cm of the geometric center of the detector along the beam direction, and within 2 cm in the transverse plane. Because of pileup the selected event can have several reconstructed vertices.
For the analysis at 8 TeV the vertex with the largest sum of the p2T of the tracks associated to it
is chosen as the primary pp interaction vertex, while at 13 TeV the reconstructed vertex with
the largest value of summed physics-object p2T is taken to be the primary vertex. The physics
objects are the objects returned by a jet finding algorithm [33, 34] applied to all charged tracks
associated with the vertex, and the associated missing pT, taken as the negative vector sum of
the pT of those jets. Events with leptons are selected by requiring each lepton track to have
a transverse impact parameter, with respect to the primary vertex, smaller than 0.5 cm and a longitudinal impact parameter smaller than 1.0 cm.
Electrons are measured in the range|η| <2.5 by using both the tracking system and the ECAL.
They are identified by means of a multivariate discriminant that includes observables sensi-tive to bremsstrahlung along the electron trajectory, the geometrical and momentum-energy agreement between the electron track and the associated energy cluster in the ECAL, the shape of the electromagnetic shower, and variables that discriminate against electrons originating
from photon conversions [35]. The momentum resolution for electrons with pT ≈45 GeV from
Z→e+e−decays ranges from 1.7% for nonshowering electrons in the barrel region to 4.5% for
showering electrons in the endcaps [35].
Muons are reconstructed in the range |η| < 2.4 by combining information from the silicon
tracker and the muon system [36]. The matching between the inner and outer tracks proceeds either outside-in, starting from a track in the muon system, or inside-out, starting from a track in the silicon tracker. The muons are selected among the reconstructed muon track candidates by applying minimal requirements on the track in both the muon system and the inner tracker system, and taking into account the compatibility with minimum-ionizing particle energy
de-posits in the calorimeters. In the intermediate range of 20 < pT < 100 GeV, matching muons
to tracks measured in the silicon tracker results in a relative pT resolution of 1.3–2.0% in the
barrel, and better than 6% in the endcaps. The pTresolution in the barrel is better than 10% for
Electrons (muons) are considered candidates for inclusion in the four-lepton final states if they
have p`T > 7(5)GeV and |η`| < 2.5(2.4). In order to suppress electrons from photon
con-versions and muons originating from in-flight decays of hadrons, we place a requirement on the impact parameter computed in three dimensions. We require that the ratio of the impact parameter for the track and its uncertainty to be less than 4. To discriminate between prompt leptons from Z boson decay and those arising from electroweak decays of hadrons within jets, an isolation requirement for leptons is imposed. The relative isolation is defined as
Riso=
∑
charged hadrons pT + max 0,∑
neutral hadrons pT +∑
photons pT − pPUT p`T, (1)where the sums run over the charged and neutral hadrons, and photons, in a cone defined by
∆R≡√(∆η)2+ (∆φ)2around the lepton trajectory. The radius∆R is set to be 0.4 and 0.3 in the
8 and 13 TeV data analyses, respectively. To minimize the contribution of charged particles from pileup to the isolation calculation, charged hadrons are included only if they originate from the primary vertex. The contributions of neutral particles from pileup to the activity inside the
cone around a lepton is referred to as pPU
T , and is obtained with different methods for electrons
and muons. For electrons, pPUT is evaluated with the jet area method described in Ref. [37]. For
muons, it is taken to be half the sum of the pT of all charged particles in the cone originating
from pileup vertices. The factor of one-half accounts for the expected fraction of neutral to
charged particles in hadronic interactions. A lepton is considered isolated if Riso < 0.4(0.35)
in the 8 (13) TeV data analysis.
The lepton momentum scales are calibrated in bins of pT` and η` using the decay products of
known resonances decaying to lepton pairs. The measured lepton momentum scale is corrected
with a Z → `+`−sample, by matching the peak of the reconstructed dilepton mass spectrum
to the nominal value of mZ [38]. Muon momenta are calibrated by using J/ψ decays as well.
We account for final-state radiation of leptons by correcting their momenta with photons of
pT > 2 GeV and within a cone of∆R = 0.5 around the lepton momentum direction [39, 40].
The photons selected by this algorithm are excluded from the lepton isolation computation. The efficiency of the lepton reconstruction and selection is measured with the tag–and–probe
technique [41] in bins of p`T and η`. This measurement is used to correct the simulation
effi-ciency.
Jets are reconstructed from particle candidates by means of the anti-kTclustering algorithm [33],
as implemented in the FASTJET package [34], with a distance parameter of 0.5 (0.4) in the
8 (13) TeV data analysis. The jet energy resolution amounts typically to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV.
Jet energy corrections are extracted from the data and the simulated events by combining sev-eral measurements and methods that account for the effects of pileup, non-uniform detector response, and residual data-simulation jet energy scale (JES) differences. The JES
calibra-tion [42, 43] relies on correccalibra-tions parametrized in terms of the uncorrected pT and η of the
jet, and are applied as multiplicative factors to the four-momentum vector of each jet.
In order to maximize the reconstruction efficiency while reducing the instrumental background and contamination from pileup jets, loose identification quality criteria [44] are imposed on jets, based on the energy fraction carried by charged and neutral hadrons, as well as charged
leptons and photons. A minimum threshold of 30 GeV on the pT of jets is required to ensure
that they are well measured and to reduce the pileup contamination. Jets are required to have
|η| < 4.7 and to be separated from all selected lepton candidates by at least∆R= 0.5(0.4)in
A signal event must contain at least two Z/γ∗ candidates, each reconstructed from a pair of
isolated electrons or muons of opposite charges. The highest-pTlepton must have pT >20 GeV,
and the second-highest lepton peT > 10(12)GeV if it is an electron, or pµT > 10 GeV in case
of a muon for the analysis at √s = 8(13)TeV. All leptons are required to be separated by
∆R(`,`0) >0.02, and electrons are required to be separated from muons by∆R(e, µ) >0.05.
Within each event, all permutations of oppositely charged leptons giving a valid pair of Z/γ∗
candidates are considered separately. For each 4`candidate, the lepton pair with the invariant
mass closest to the nominal Z boson mass is denoted by Z1and the other dilepton candidate is
denoted by Z2. Both Z1and Z2are required to have a mass between 60 and 120 GeV. All pairs
of oppositely charged leptons in the 4`candidate are required to have m``0 >4 GeV regardless
of their flavor to remove contributions from the decay of low-mass hadron resonances.
If multiple 4`candidates within an event pass this selection, the candidate with mZ1 closest to
the nominal Z boson mass is chosen. In the rare cases (0.3%) of further ambiguity, which may
arise in events with more than 4 leptons, the Z2candidate that maximizes the scalar pT sum of
the four leptons is chosen. The set of selection criteria just described is referred to as the ZZ
selection, and gives a total of 288 (927) observed events at√s=8(13)TeV. The corresponding
number of expected signal events from MC prediction is about 271 (850).
5
Background estimation
The largest source of background arises from processes in which heavy-flavor jets produce secondary leptons, and from processes in which jets are misidentified as leptons. The main contributing processes are Z+jets, tt, and WZ+jets.
However, the lepton identification and isolation requirements reduce this background to a very small level compared to the signal. The residual contribution is estimated from data samples
consisting of Z +``events that are required to pass the ZZ selection described in Section 4,
ex-cept that either one or both leptons belonging to the Z2candidate fail the isolation or
identifica-tion requirements. Two control samples are selected, with one and two misidentified leptons, respectively. The background yield in the signal region is estimated by weighting the number of events in the control samples by the lepton misidentification rate measured in data in a ded-icated control region. The procedure is identical to that of Refs. [7, 8] and is described in more detail in Ref. [39].
Another source of background arises from processes that produce four genuine high-pT
iso-lated leptons, pp→ttZ and pp→WWZ. This contribution is small and is estimated by using
the corresponding simulated samples.
The total estimated background yields are 8±4 (37±11) events in the 8 (13) TeV signal region.
6
Systematic uncertainties
The systematic uncertainties are estimated by varying the quantities that may affect the cross section and by propagating the changes to the analysis procedure. The systematic uncertainties from sources that may affect the differential cross section shapes have been estimated through the unfolding procedure by recomputing the response matrix, after varying each source of systematic uncertainty independently and in both directions, up and down. The systematic uncertainties in the differential cross section as a function of the jet multiplicity are summarized in Table 1. Those that depend on the number of jets in the event are listed as a range.
The systematic uncertainty in the trigger efficiency is evaluated by taking the difference be-tween the value obtained from the data and that from the simulated events, and it leads to a 1.5 (2.0)% uncertainty in the differential cross sections measured with the 8 (13) TeV data. The uncertainties arising from lepton reconstruction and selection (identification, isolation, and im-pact parameter determination) depend on the jet multiplicity, are sensitive to statistical fluc-tuations, and range between 0.9 and 4.4%, in the 8 TeV analysis (3.7 and 4.5%, in the 13 TeV analysis). The largest contribution to the systematic uncertainty in the differential cross section measurements comes from the JES determination, which increases with the jet multiplicity and reaches 9.2 (17.5)% when the number of jets exceeds two in the 8 (13) TeV analysis. Likewise, the uncertainty due to the jet energy resolution (JER) increases from 0.2 to 1.7% (2.1 to 8.4%) for the 8 (13) TeV samples. The larger JES and JER uncertainties for the 13 TeV sample reflect the
increase in the number of soft jets (with pT close to the 30 GeV threshold) as a function of the
center-of-mass energy.
The uncertainties in the Z+jets, WZ+jets, and tt background have two components, which are added in quadrature. The first relates to the different relative fraction of these background processes in the control sample where we measure the lepton misidentification rate and the sample to which this rate is applied. The second is the statistical uncertainty in the control sample. The effect of these uncertainties increases with the jet multiplicity and amounts to 0.7–6.9% (0.5–2.4%) in the 8 (13) TeV measurement. The contribution to the uncertainty from the modeling of genuine four lepton background is smaller and varies between 0.1 and 2.0%
(<0.1 and 1.2%) for the 8 (13) TeV data. The pileup uncertainty is evaluated by varying the
pileup modeling in the MC samples within its uncertainty. The uncertainty in the integrated luminosity is 2.6 [45] and 2.5% [46] for the 8 and 13 TeV data, respectively.
The contribution of the MC generator choice to the systematic uncertainty is obtained by
com-paring the results found with two different sets of MC samples: MADGRAPH5 + MCFM +
PHANTOM (MG5 aMC@NLO + MCFM + PHANTOM) and POWHEG + MCFM + PHANTOM for
the 8 (13) TeV measurement, and ranges from 0.2 to 3.7% (0.5 to 5.0%) at 8 (13) TeV. The impact
of the relative contribution of the qq→ZZ and gg→ZZ processes in the response matrix
def-inition is less than 1% and is evaluated by varying the corresponding cross section within their renormalization and factorization scale uncertainties. For 8 TeV, where no LO to NLO factor is
applied to theMCFMcross section, the gg→ZZ cross section is varied by 100% of its value. The
statistical uncertainties of the MC samples result in negligible contributions to the response ma-trix uncertainty. The systematic uncertainty arising from the choice of the PDF and the strong
coupling strength αShas been evaluated using the PDF4LHC recommendations [47–49], using
the CT10, MSTW08, and NNPDF2.3 [50] PDF sets, in the 8 TeV analysis, and the NNPDF3.0 set in the 13 TeV analysis.
The total systematic uncertainty is obtained by summing all the sources in quadrature, taking into account the correlations among the different channels.
For the normalized differential cross sections, only systematic uncertainties affecting the shape of the distributions are relevant. The uncertainties in the luminosity and trigger efficiency cancel out completely, as well as other contributions to the uncertainty in the total yield.
7
The ZZ+jets differential cross section measurements
The distributions of the jet multiplicity combining the 4µ, 4e, and 2µ2e channels are shown in Fig. 1, together with the SM expectations, the estimated backgrounds, and the systematic uncertainty in the prediction.
Table 1: The contributions to the uncertainty in the absolute and normalized differential cross section measurements in Fig. 2 and 3, upper panels. Uncertainties that depend on jet multiplic-ity are listed as a range.
8 TeV data 13 TeV data
Systematic source Absolute (%) Normalized (%) Absolute (%) Normalized (%)
Trigger 1.5 — 2.0 —
Lepton reconstruction and selection 0.9–4.4 ≤0.1 3.7–4.5 0.1–0.8
Jet energy scale 1.5–9.2 1.5–9.1 4.6–17.5 4.6–17.5
Jet energy resolution 0.2–1.7 0.2–1.7 2.1–8.4 2.1–8.4
Background yields 0.7–7.2 0.7–5.4 0.5–2.8 0.4–2.0
Pileup 1.8 1.8 0.3–1.9 0.6–1.8
Luminosity 2.6 — 2.5 —
Choice of Monte Carlo generators 0.2–3.7 0.2–3.7 0.5–5.0 0.8–4.7 qq/gg cross section 0.1–0.8 0.1–0.8 <0.1–0.3 0.1–0.2 PDF 1.0 — <0.1–0.2 <0.1–0.2 αS <0.1 <0.1 ≤0.1 ≤0.1 jets N 0 1 2 ≥ 3 Events 1 10 2 10 3 10 Data Syst ZZ(+jets) → qq ZZ → gg ZZ+2 jets (EW) → qq Z t WWZ,t t Z+X,t (8 TeV) -1 19.7 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.5) Jets T anti-k jets N 0 1 2 3 ≥ 4 Events 10 2 10 3 10 Data Syst ZZ(+jets) → qq ZZ → gg ZZ+2 jets (EW) → qq Z t WWZ,t t Z+X,t (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k
Figure 1: Distribution of the reconstructed jet multiplicity in the 8 TeV (left) and 13 TeV (right) data. The points represent the data and the vertical bars correspond to the statistical uncer-tainty. The shaded histograms represent MC predictions and the background estimates, while the hatched band on their sum indicates the systematic uncertainty of the prediction. The Z+jets and tt background is obtained from the data.
The differential pp → ZZ → ```0`0 cross section is measured as a function of the jet
multi-plicity, the pT-leading jet transverse momentum (pj1T) and pseudorapidity (ηj1) with the 8 and
13 TeV data. Because of the limited number of events with more than one jet at 8 TeV, the
dif-ferential cross section as a function of the pT-subleading jet transverse momentum (pj2T) and
pseudorapidity (ηj2), as well as the invariant mass of the two pT-leading jets (mjj) and their
pseudorapidity separation (∆ηjj) are studied at 13 TeV only. For all measurements we consider
jets with pjT > 30 GeV and|ηj| < 4.7. For the jet multiplicity distribution we also present the
measurements made with central jets (|ηj| < 2.4) only. The measurements are performed for
the two slightly different phase space regions adopted for the 8 [6] and 13 [8] TeV data, which are given in Table 2. The generator-level lepton momenta are corrected by adding the
the same method adopted to extract the signal at the reconstruction level. In order to define the
jets at generator level, the generated particles are clustered using the anti-kTalgorithm, with a
distance parameter identical to the corresponding one at reconstruction level.
Table 2: Phase space definitions for cross section measurements at 8 TeV [6] and 13 TeV [8]. The common definitions apply to both measurements.
8 TeV 13 TeV peT >7 GeV,|ηe| <2.5 peT >5 GeV,|ηe| <2.5 pµT >5 GeV,|ηµ| <2.4 pµT >5 GeV,|ηµ| <2.5 Common definitions p`1 T >20 GeV , p `2 T >10 GeV
m`+`− >4 GeV (any opposite-sign same-flavor pair)
60< (mZ1, mZ2) <120 GeV
Each distribution is corrected for the event selection efficiency and the detector resolution ef-fects by means of a response matrix that translates the physics variables at generator level into their reconstructed values. The correction procedure is based on the iterative D’Agostini
un-folding method technique [51], as implemented in the ROOUNFOLDtoolkit [52], and
regular-ized by stopping after four iterations. The robustness of the result is tested against the singular value decomposition (SVD) [53] alternative unfolding method. For each measured distribu-tion, a response matrix is evaluated using two different sets of generators: the first one includes
MADGRAPH5 (qq → ZZ), MCFM(gg → ZZ) and PHANTOM (qq → ZZ + 2 jets) for the 8 TeV
data set and MG5 aMC@NLO(qq→ZZ),MCFM(gg→ZZ) and PHANTOM(qq→ZZ + 2 jets)
for the 13 TeV data set. In the second one, thePOWHEGsample is instead used for the qq→ZZ
process in both the 8 and 13 TeV data analyses. The former set, where the leading-order MC generator can simulate up to two jets at matrix-element level, is taken as the reference, while the latter is used for comparison and to estimate the systematic uncertainty due to the MC
gen-erator choice. After the unfolding, the cross sections for pp → ZZ+N jets → ```0`0+N jets,
for N =0, 1, 2, and≥3, are extracted.
The differential cross sections as a function of the jet multiplicity are shown in Fig. 2 for|ηj| <
4.7 (upper) and for |ηj| < 2.4 (lower). The ratios between the measured and expected
distri-butions from the MADGRAPH5, MG5 aMC@NLO, andPOWHEGset of samples for√s=8 TeV,
andPOWHEGand MG5 aMC@NLOfor√s =13 TeV are also shown in the figures. Uncertainties in the MC predictions at the matrix-element level are evaluated by varying the renormalization and factorization scales independently, up and down, by a factor of two with respect to the
de-fault values of µR =µF =m4` forPOWHEGand µR= µF= 12∑ pjT+∑ p`T for MG5 aMC@NLO.
In theMCFMpredictions, the uncertainty in the LO to NLO cross section scaling factor includes
the renormalization and factorization scales uncertainty. The theoretical uncertainties also
in-clude the uncertainties in the PDF and αS. The measured and expected cross section values for
|ηj| <4.7 are given in Tables 3 and 4.
The differential distributions, normalized to the cross sections, are presented in Figs. 3–6 to-gether with the theoretical predictions. For the theoretical predictions, only the uncertainty in the shape is included, which yields a smaller uncertainty compared to the unnormalized case. Figure 3 (top panels) shows the normalized differential cross section as a function of the jet
mul-tiplicity, with|ηj| < 4.7. The observed fraction of events in the first bin with zero jets is larger
than the predicted value, while for 1, 2, and ≥3 jets, the fraction is lower. Better agreement
is observed for |ηj| < 2.4 (Fig. 3, bottom panels). The measurements of the differential cross
Table 3: The pp → ZZ → ```0`0 cross section at √s = 8 TeV as a function of the jet
multi-plicity. The integrated luminosity uncertainty for number of jets = 2 and≥3 is negligible and
not quoted. The cross sections are compared to the theoretical predictions (last column) from
MG5 aMC@NLO+MCFM+ PHANTOM.
Number of jets (|ηj| <4.7) Cross section [fb] Theoretical cross section [fb]
0 16.3±1.2 (stat)+1.0−0.9(syst)±0.4 (lumi) 13.2+0.9−0.7
1 3.2±0.6 (stat)+0.3−0.3(syst)±0.1 (lumi) 4.0+0.5−0.3
2 0.7±0.3 (stat)+0.1−0.1(syst) 1.2+0.2−0.1
≥3 0.14±0.1 (stat)+0.01−0.01(syst) 0.3+0.1−0.1
Table 4: The pp→ZZ→ ```0`0cross section at√s=13 TeV as a function of the jet multiplicity.
The integrated luminosity uncertainty for the number of jets≥3 is smaller than 0.1 fb and is
not quoted. The cross sections are compared to the theoretical predictions (last column) from
MG5 aMC@NLO+MCFM+ PHANTOM.
Number of jets (|ηj| <4.7) Cross section [fb] Theoretical cross section [fb]
0 28.3±1.3 (stat)+1.7−1.5(syst)±0.7 (lumi) 23.6+0.8−0.9
1 8.0±0.8 (stat)+0.7−0.8(syst)±0.2 (lumi) 9.7+0.5−0.5
2 3.0±0.5 (stat)+0.3−0.4(syst)±0.1 (lumi) 4.0+0.3−0.3
≥3 1.3±0.4 (stat)+0.2−0.2(syst) 1.7+0.1−0.1
at 8 and 13 TeV when NLO matrix-element calculations are used in conjunction withPYTHIA8
for parton showering, hadronization, and underlying event simulation. In the data, jets tend to
have a lower pTvalue than in the simulations and therefore, on average, they are less likely to
pass the 30 GeV threshold, thus increasing the number of events with no jets. The observation of fewer events than expected with at least one jet can be ascribed to a softer distribution of the transverse momentum of the hadronic particles recoiling against the diboson system. This
explanation is supported by the measurement of a softer-than-expected pT distribution of the
ZZ system [6, 8]. The observed discrepancy may be due to higher-order corrections to ZZ pro-duction, not included in MC samples used in this analysis, or to the parton shower modeling. Figure 4 shows the differential cross sections at 8 and 13 TeV as functions of the transverse
mo-mentum and pseudorapidity of the pT-leading jet, normalized to the cross section for Njets ≥1.
Figures 5 and 6 show the cross section at 13 TeV as a function of several variables for events with
Njets ≥2, normalized to the corresponding cross section. More specifically, Fig. 5 presents the
normalized differential cross sections as functions of the transverse momentum and
pseudora-pidity of the pT-subleading jet, while Fig. 6 displays the differential cross section as a function
of mjjand∆ηjj.
Overall agreement is observed between data and theoretical predictions for all measurements
related to the pT-leading and subleading jets. The∆ηjjdistribution (Fig. 6, right) measured with
13 TeV data tends to be steeper than the MC predictions, but the differences are not statistically significant.
8
Summary
The differential cross sections for the production of Z pairs in the four-lepton final state in
as-sociation with jets in proton-proton collisions at√s = 8 and 13 TeV have been measured. The
data correspond to an integrated luminosity of 19.7 (35.9) fb−1 for a center-of-mass energy of
func-0 1 2 ≥ 3 [fb] jets dN σ d 1 − 10 1 10 2 10
Unfolded data + stat. uncertainty
syst. eval uncertainty ⊕ Stat. MadGraph+MCFM+Pythia6 MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia6 (8 TeV) -1 19.7 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.5) Jets T anti-k 0 1 2 ≥ 3 Data/MC 0 1 2 MadGraph+MCFM+Pythia6 jets N 0 1 2 ≥ 3 Data/MC 0 1 2 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 0 1 2 Powheg+MCFM+Pythia6. jets N [fb] jets dN σ d 1 10
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 0.5 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 0.5 1 1.5 Powheg+MCFM+Pythia8. jets N 0 1 2 ≥ 3 [fb] jets dN σ d 1 − 10 1 10 2 10
Unfolded data + stat. uncertainty
syst. eval uncertainty ⊕ Stat. MadGraph+MCFM+Pythia6 MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia6 (8 TeV) -1 19.7 fb CMS |<2.4 j η >30 GeV, | j T p (R=0.5) Jets T anti-k 0 1 2 ≥ 3 Data/MC 0 1 MadGraph+MCFM+Pythia6 jets N 0 1 2 ≥ 3 Data/MC 0 1 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 0 1 Powheg+MCFM+Pythia6. jets N [fb] jets dN σ d 1 10 2 10
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<2.4 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 1 1.5 Powheg+MCFM+Pythia8. jets N
Figure 2: Differential cross sections of pp → ZZ → 4`as a function of the multiplicity of jets
with |ηj| < 4.7 (top panels) and |ηj| < 2.4 (bottom panels), for the 8 (left) and 13 (right) TeV
data. The measurements are compared to the predictions of MG5 aMC@NLO, POWHEG, and
MADGRAPH5 (8 TeV only) sets of samples. Each MC set, along with the main MC generator,
includes the MCFM and PHANTOM generators. PYTHIA 6 and PYTHIA 8 are used for parton
showering, hadronization, and underlying event simulation, for the 8 and 13 TeV analysis,
re-spectively, with the sole exception of MG5 aMC@NLO, which is always interfaced to PYTHIA
8. The total experimental uncertainties are shown as hatched regions, while the colored bands display the theoretical uncertainties in the matrix-element calculations.
0 1 2 ≥ 3 jets dN σ d σ 1 2 − 10 1 − 10 1 10
Unfolded data + stat. uncertainty
syst. eval uncertainty ⊕ Stat. MadGraph+MCFM+Pythia6 MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia6 (8 TeV) -1 19.7 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.5) Jets T anti-k 0 1 2 ≥ 3 Data/MC 0 1 MadGraph+MCFM+Pythia6 jets N 0 1 2 ≥ 3 Data/MC 0 1 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 0 1 Powheg+MCFM+Pythia6. jets N jets dN σ d σ 1 1 − 10 1
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 0.5 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 0.5 1 1.5 Powheg+MCFM+Pythia8. jets N 0 1 2 ≥ 3 jets dN σ d σ 1 2 − 10 1 − 10 1 10
Unfolded data + stat. uncertainty
syst. eval uncertainty ⊕ Stat. MadGraph+MCFM+Pythia6 MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia6 (8 TeV) -1 19.7 fb CMS |<2.4 j η >30 GeV, | j T p (R=0.5) Jets T anti-k 0 1 2 ≥ 3 Data/MC 0 0.5 1 1.5 MadGraph+MCFM+Pythia6 jets N 0 1 2 ≥ 3 Data/MC 0 0.5 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 0 0.5 1 1.5 Powheg+MCFM+Pythia6. jets N jets dN σ d σ 1 2 − 10 1 − 10 1
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<2.4 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 1 2 ≥ 3 Data/MC 1 1.5 Powheg+MCFM+Pythia8. jets N
Figure 3: Differential cross sections normalized to the cross section of pp → ZZ → 4` as a
function of the multiplicity of jets with|ηj| <4.7 (top panels) and |ηj| < 2.4 (bottom panels),
50 100 150 200 250 300 [1/GeV] j1 T dp σ d 1 ≥ jets σ 1 4 − 10 3 − 10 2 − 10 1 −
10 Unfolded data + stat. uncertainty
syst. eval uncertainty ⊕ Stat. MadGraph+MCFM+Pythia6 MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia6 (8 TeV) -1 19.7 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.5) Jets T anti-k 50 100 150 200 250 300 Data/MC 0 2 4 MadGraph+MCFM+Pythia6 [GeV] j1 T p 50 100 150 200 250 300 Data/MC 0 2 4 MG5_aMC@NLO+MCFM+Pythia8. 50 100 150 200 250 300 Data/MC 0 2 4 Powheg+MCFM+Pythia6. [GeV] j1 T p [1/GeV] j1 T dp σ d 1 ≥ jets σ 1 4 − 10 3 − 10 2 − 10
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 1 2 MG5_aMC@NLO+MCFM+Pythia8. 50 100 150 200 250 300 350 400 450 500 Data/MC 1 2 Powheg+MCFM+Pythia8. [GeV] j1 T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 | j1 η d| σ d 1 ≥ jets σ 1 0 0.1 0.2 0.3 0.4 0.5 0.6
Unfolded data + stat. uncertainty
syst. eval uncertainty ⊕ Stat. MadGraph+MCFM+Pythia6 MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia6 (8 TeV) -1 19.7 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.5) Jets T anti-k 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data/MC 0 1 2 MadGraph+MCFM+Pythia6 | j1 η | 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data/MC 0 1 2 MG5_aMC@NLO+MCFM+Pythia8. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data/MC 0 1 2 Powheg+MCFM+Pythia6. | j1 η | | j1 η d| σ d 1 ≥ jets σ 1 0 0.1 0.2 0.3 0.4 0.5
0.6 Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 0.5 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data/MC 0.5 1 1.5 Powheg+MCFM+Pythia8. | j1 η |
Figure 4: Differential cross sections normalized to the cross section for Njets ≥1 of pp→ZZ→
4`as a function of the pT-leading jet transverse momentum (top panels) and the absolute value
of the pseudorapidity (bottom panels), for the 8 (left) and 13 (right) TeV data. Other details are as described in the caption of Fig. 2.
[1/GeV] j2 T dp σ d 2 ≥ jets σ 1 4 − 10 3 − 10 2 − 10
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 1 2 3 MG5_aMC@NLO+MCFM+Pythia8. 50 100 150 200 250 300 Data/MC 1 2 3 Powheg+MCFM+Pythia8. [GeV] j2 T p | j2 η d| σ d 2 ≥ jets σ 1 0 0.1 0.2 0.3 0.4
0.5 Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 0.5 1 1.5 MG5_aMC@NLO+MCFM+Pythia8. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data/MC 0.5 1 1.5 Powheg+MCFM+Pythia8. | j2 η |
Figure 5: Differential cross sections normalized to the cross section for Njets ≥2 of pp→ZZ→
4` at√s = 13 TeV as a function of the pT-subleading jet transverse momentum (left) and the
absolute value of the pseudorapidity (right). Other details are as described in the caption of Fig. 2. [1/GeV] jj dm σ d 2 ≥ jets σ 1 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 1 2 MG5_aMC@NLO+MCFM+Pythia8. 0 200 400 600 800 1000 Data/MC 1 2 Powheg+MCFM+Pythia8. [GeV] jj m jj η∆ d σ d 2 ≥ jets σ 1 0 0.1 0.2 0.3 0.4 0.5 0.6
Unfolded data + stat. uncertainty
syst. uncertainty ⊕ Stat. MG5_aMC@NLO+MCFM+Pythia8 Powheg+MCFM+Pythia8 (13 TeV) -1 35.9 fb CMS |<4.7 j η >30 GeV, | j T p (R=0.4) Jets T anti-k Data/MC 0 1 2 MG5_aMC@NLO+MCFM+Pythia8. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data/MC 0 1 2 Powheg+MCFM+Pythia8. jj η ∆
Figure 6: Differential cross sections normalized to the cross section for Njets ≥2 of pp→ZZ→
4`at√s =13 TeV as a function of the invariant mass of the two pT-leading jets (left) and their
tion of the number of jets, the transverse momentum pT, and pseudorapidity of the pT-leading
and subleading jets. Distributions of the invariant mass of the two pT-leading jets and their
separation in pseudorapidity are also presented. Good agreement is observed between the measurements and the theoretical predictions when next-to-leading order matrix-element
cal-culations are used together with thePYTHIAparton shower simulation. Cross sections for ZZ
production in association with jet have been measured with a precision ranging from 10 to 72%
(8 to 38%) at 8 (13) TeV, for jet multiplicities ranging from 0 to≥3. The systematic uncertainty
is of the same size, or smaller, than the statistical one. Analyses using future, larger data sets, with smaller statistical uncertainties, will allow the theoretical prediction of ZZ+jets to undergo more stringent tests.
Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we grate-fully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Fi-nally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Aus-tria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Ger-many); GSRT (Greece); NKFIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS and RFBR (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI and FEDER (Spain); Swiss Fund-ing Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE and NSF (USA).
Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, contract No. 675440 (European Union); the Leventis Foun-dation; the A. P. Sloan FounFoun-dation; the Alexander von Humboldt FounFoun-dation; the Belgian Fed-eral Science Policy Office; the Fonds pour la Formation `a la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWTBelgium); the F.R.S.FNRS and FWO (Belgium) under the “Excellence of Science EOS” -be.h project n. 30820817; the Ministry of Education, Youth and Sports (MEYS) of the Czech Re-public; the Lend ¨ulet (“Momentum”) Program and the J´anos Bolyai Research Scholarship of the
Hungarian Academy of Sciences, the New National Excellence Program ´UNKP, the NKFIA
re-search grants 123842, 123959, 124845, 124850 and 125105 (Hungary); the Council of Science and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the National Priorities Research Program by Qatar National Research Fund; the Programa Estatal de Fomento de la Investi-gaci ´on Cient´ıfica y T´ecnica de Excelencia Mar´ıa de Maeztu, grant MDM-2015-0509 and the
Pro-grama Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programs cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Ad-vancement Project (Thailand); the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).
References
[1] M. Lemoine and M. J. G. Veltman, “Radiative corrections to e+e−→W+W−in the
Weinberg model”, Nucl. Phys. B 164 (1980) 445, doi:10.1016/0550-3213(80)90521-0.
[2] ATLAS Collaboration, “Measurement of ZZ production in pp collisions at√s=7 TeV
and limits on anomalous ZZZ and ZZγ couplings with the ATLAS detector”, JHEP 03 (2013) 128, doi:10.1007/JHEP03(2013)128, arXiv:1211.6096.
[3] ATLAS Collaboration, “Measurement of the ZZ production cross section in pp collisions
at√s=13 TeV with the ATLAS detector”, Phys. Rev. Lett. 116 (2016) 101801,
doi:10.1103/PhysRevLett.116.101801, arXiv:1512.05314.
[4] ATLAS Collaboration, “ZZ→ `+`−`0+`0−cross-section measurements and search for
anomalous triple gauge couplings in 13 TeV pp collisions with the ATLAS detector”, Phys. Rev. D 97 (2018) 032005, doi:10.1103/PhysRevD.97.032005,
arXiv:1709.07703.
[5] CMS Collaboration, “Measurement of the ZZ production cross section and search for
anomalous couplings in 2`2`0 final states in pp collisions at√s=7 TeV”, JHEP 01 (2013)
063, doi:10.1007/JHEP01(2013)063, arXiv:1211.4890.
[6] CMS Collaboration, “Measurement of the pp→ZZ production cross section and
constraints on anomalous triple gauge couplings in four-lepton final states at√s=
8 TeV”, Phys. Lett. B 740 (2015) 250, doi:10.1016/j.physletb.2014.11.059,
arXiv:1406.0113. [Erratum: doi:10.1016/j.physletb.2016.04.010].
[7] CMS Collaboration, “Measurement of the ZZ production cross section and Z
→ `+`−`0+`0− branching fraction in pp collisions at√s=13 TeV”, Phys. Lett. B 763
(2016) 280, doi:10.1016/j.physletb.2016.10.054, arXiv:1607.08834.
[8] CMS Collaboration, “Measurements of the pp→ZZ production cross section and the
Z√→4`branching fraction, and constraints on anomalous triple gauge couplings at
s =13 TeV”, Eur. Phys. J. C 78 (2018) 165,
doi:10.1140/epjc/s10052-018-5567-9, arXiv:1709.08601.
[9] CMS Collaboration, “Measurement of vector boson scattering and constraints on
anomalous quartic couplings from events with four leptons and two jets in proton-proton
collisions at√s = 13 TeV”, Phys. Lett. B 774 (2017) 682,
doi:10.1016/j.physletb.2017.10.020, arXiv:1708.02812.
[10] CMS Collaboration, “Description and performance of track and primary-vertex reconstruction with the CMS tracker”, JINST 9 (2014) P10009,
[11] CMS Collaboration, “The CMS trigger system”, JINST 12 (2017) P01020, doi:10.1088/1748-0221/12/01/P01020, arXiv:1609.02366.
[12] CMS Collaboration, “The CMS experiment at the CERN LHC”, JINST 3 (2008) S08004,
doi:10.1088/1748-0221/3/08/S08004.
[13] J. Alwall et al., “Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions”, Eur. Phys. J. C 53 (2008) 473,
doi:10.1140/epjc/s10052-007-0490-5, arXiv:0706.2569.
[14] J. Alwall et al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations”, JHEP 07 (2014) 079, doi:10.1007/JHEP07(2014)079, arXiv:1405.0301.
[15] T. Melia, P. Nason, R. R ¨ontsch, and G. Zanderighi, “W+W−, WZ and ZZ production in
the POWHEG BOX”, JHEP 11 (2011) 078, doi:10.1007/JHEP11(2011)078, arXiv:1107.5051.
[16] P. Nason, “A new method for combining NLO QCD with shower Monte Carlo algorithms”, JHEP 11 (2004) 040, doi:10.1088/1126-6708/2004/11/040, arXiv:hep-ph/0409146.
[17] S. Frixione, P. Nason, and C. Oleari, “Matching NLO QCD computations with parton shower simulations: the POWHEG method”, JHEP 11 (2007) 070,
doi:10.1088/1126-6708/2007/11/070, arXiv:0709.2092.
[18] S. Alioli, P. Nason, C. Oleari, and E. Re, “A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX”, JHEP 06 (2010) 043,
doi:10.1007/JHEP06(2010)043, arXiv:1002.2581.
[19] R. Frederix and S. Frixione, “Merging meets matching in MC@NLO”, JHEP 12 (2012) 061, doi:10.1007/JHEP12(2012)061, arXiv:1209.6215.
[20] F. Cascioli et al., “ZZ production at hadron colliders in NNLO QCD”, Phys. Lett. B 735 (2014) 311, doi:10.1016/j.physletb.2014.06.056, arXiv:1405.2219.
[21] J. M. Campbell and R. K. Ellis, “MCFM for the Tevatron and the LHC”, Nucl. Phys. B Proc. Suppl. 10 (2010) 205, doi:10.1016/j.nuclphysbps.2010.08.011,
arXiv:1007.3492.
[22] F. Caola, K. Melnikov, R. R ¨ontsch, and L. Tancredi, “QCD corrections to ZZ production in gluon fusion at the LHC”, Phys. Rev. D 92 (2015) 094028,
doi:10.1103/PhysRevD.92.094028, arXiv:1509.06734.
[23] A. Ballestrero et al., “PHANTOM: A Monte Carlo event generator for six parton final states at high energy colliders”, Comput. Phys. Commun. 180 (2009) 401,
doi:10.1016/j.cpc.2008.10.005, arXiv:0801.3359.
[24] T. Sj ¨ostrand, S. Mrenna, and P. Skands, “PYTHIA 6.4 physics and manual”, JHEP 05 (2006) 026, doi:10.1088/1126-6708/2006/05/026, arXiv:hep-ph/0603175. [25] CMS Collaboration, “Study of the underlying event at forward rapidity in pp collisions
at√s = 0.9, 2.76, and 7 TeV”, JHEP 04 (2013) 072, doi:10.1007/JHEP04(2013)072,
[26] T. Sj ¨ostrand et al., “An introduction to PYTHIA 8.2”, Comput. Phys. Commun. 191 (2015) 159, doi:10.1016/j.cpc.2015.01.024, arXiv:1410.3012.
[27] H.-L. Lai et al., “Uncertainty induced by QCD coupling in the CTEQ global analysis of parton distributions”, Phys. Rev. D 82 (2010) 054021,
doi:10.1103/PhysRevD.82.054021, arXiv:1004.4624.
[28] H.-L. Lai et al., “New parton distributions for collider physics”, Phys. Rev. D 82 (2010) 074024, doi:10.1103/PhysRevD.82.074024, arXiv:1007.2241.
[29] CMS Collaboration, “Event generator tunes obtained from underlying event and multiparton scattering measurements”, Eur. Phys. J. C 76 (2016) 155,
doi:10.1140/epjc/s10052-016-3988-x, arXiv:1512.00815.
[30] NNPDF Collaboration, “Parton distributions for the LHC run II”, JHEP 04 (2015) 040, doi:10.1007/JHEP04(2015)040, arXiv:1410.8849.
[31] GEANT4 Collaboration, “GEANT4 — a simulation toolkit”, Nucl. Instrum. Meth. A 506
(2003) 250, doi:10.1016/S0168-9002(03)01368-8.
[32] CMS Collaboration, “Particle-flow reconstruction and global event description with the CMS detector”, JINST 12 (2017) P10003, doi:10.1088/1748-0221/12/10/P10003,
arXiv:1706.04965.
[33] M. Cacciari, G. P. Salam, and G. Soyez, “The anti-ktjet clustering algorithm”, JHEP 04
(2008) 063, doi:10.1088/1126-6708/2008/04/063, arXiv:0802.1189.
[34] M. Cacciari, G. P. Salam, and G. Soyez, “FastJet user manual”, Eur. Phys. J. C 72 (2012) 1896, doi:10.1140/epjc/s10052-012-1896-2, arXiv:1111.6097.
[35] CMS Collaboration, “Performance of electron reconstruction and selection with the CMS
detector in proton-proton collisions at√s=8 TeV”, JINST 10 (2015) P06005,
doi:10.1088/1748-0221/10/06/P06005, arXiv:1502.02701.
[36] CMS Collaboration, “Performance of CMS muon reconstruction in pp collision events at√
s =7 TeV”, JINST 7 (2012) P10002, doi:10.1088/1748-0221/7/10/P10002,
arXiv:1206.4071.
[37] M. Cacciari and G. P. Salam, “Pileup subtraction using jet areas”, Phys. Lett. B 659 (2008) 119, doi:10.1016/j.physletb.2007.09.077, arXiv:0707.1378.
[38] The ALEPH Collaboration, the DELPHI Collaboration, the L3 Collaboration, the OPAL Collaboration, the SLD Collaboration, the LEP Electoweak Working Group, the SLD Electroweak and Heavy Flavour Groups, “Precision electroweak measurements on the Z resonance”, Phys. Rep. 427 (2006) 257, doi:10.1016/j.physrep.2005.12.006. [39] CMS Collaboration, “Measurement of the properties of a Higgs boson in the four-lepton
final state”, Phys. Rev. D 89 (2014) 092007, doi:10.1103/PhysRevD.89.092007, arXiv:1312.5353.
[40] CMS Collaboration, “Measurements of properties of the Higgs boson decaying into the
four-lepton final state in pp collisions at√s= 13 TeV”, JHEP 11 (2017) 047,
[41] CMS Collaboration, “Measurement of the inclusive W and Z production cross sections in
pp collisions at√s =7 TeV”, JHEP 10 (2011) 132, doi:10.1007/JHEP10(2011)132,
arXiv:1107.4789.
[42] CMS Collaboration, “Jet energy scale and resolution performances with 13 TeV data”, CMS Detector Performance Summary CMS-DP-2016-020, 2016.
[43] CMS Collaboration, “Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV”, JINST 12 (2017) P02014,
doi:10.1088/1748-0221/12/02/P02014, arXiv:1607.03663.
[44] CMS Collaboration, “Jet algorithms performance in 13 TeV data”, CMS Physics Analysis Summary CMS-PAS-JME-16-003, 2017.
[45] CMS Collaboration, “CMS luminosity based on pixel cluster counting — summer 2013 update”, CMS Physics Analysis Summary CMS-PAS-LUM-13-001, 2013.
[46] CMS Collaboration, “CMS luminosity measurements for the 2016 data taking period”, CMS Physics Analysis Summary CMS-PAS-LUM-17-001, 2017.
[47] M. Botje et al., “The PDF4LHC working group interim recommendations”, (2011).
arXiv:1101.0538.
[48] S. Alekhin et al., “The PDF4LHC working wroup interim report”, (2011). arXiv:1101.0536.
[49] J. Butterworth et al., “PDF4LHC recommendations for LHC Run II”, J. Phys. G 43 (2016) 023001, doi:10.1088/0954-3899/43/2/023001, arXiv:1510.03865.
[50] NNPDF Collaboration, “Impact of heavy quark masses on parton distributions and LHC phenomenology”, Nucl. Phys. B 849 (2011) 296,
doi:10.1016/j.nuclphysb.2011.03.021, arXiv:1101.1300.
[51] G. D’Agostini, “A multidimensional unfolding method based on Bayes’ theorem”, Nucl. Instrum. Meth. A 362 (1995) 487, doi:10.1016/0168-9002(95)00274-X.
[52] T. Adye, “Unfolding algorithms and tests using RooUnfold”, Proceedings, PHYSTAT 2011 Workshop on Statistical Issues Related to Discovery Claims in Search Experiments and
Unfolding, CERN,Geneva, Switzerland 17-20 January 2011 (2011) 313, doi:10.5170/CERN-2011-006.313, arXiv:1105.1160.
[53] A. H ¨ocker and V. Kartvelishvili, “SVD approach to data unfolding”, Nucl. Instrum. Meth. A 372 (1996) 469, doi:10.1016/0168-9002(95)01478-0,
A
The CMS Collaboration
Yerevan Physics Institute, Yerevan, Armenia
A.M. Sirunyan, A. Tumasyan
Institut f ¨ur Hochenergiephysik, Wien, Austria
W. Adam, F. Ambrogi, E. Asilar, T. Bergauer, J. Brandstetter, M. Dragicevic, J. Er ¨o,
A. Escalante Del Valle, M. Flechl, R. Fr ¨uhwirth1, V.M. Ghete, J. Hrubec, M. Jeitler1, N. Krammer,
I. Kr¨atschmer, D. Liko, T. Madlener, I. Mikulec, N. Rad, H. Rohringer, J. Schieck1, R. Sch ¨ofbeck,
M. Spanring, D. Spitzbart, A. Taurok, W. Waltenberger, J. Wittmann, C.-E. Wulz1, M. Zarucki
Institute for Nuclear Problems, Minsk, Belarus
V. Chekhovsky, V. Mossolov, J. Suarez Gonzalez
Universiteit Antwerpen, Antwerpen, Belgium
E.A. De Wolf, D. Di Croce, X. Janssen, J. Lauwers, M. Pieters, M. Van De Klundert, H. Van Haevermaet, P. Van Mechelen, N. Van Remortel
Vrije Universiteit Brussel, Brussel, Belgium
S. Abu Zeid, F. Blekman, J. D’Hondt, I. De Bruyn, J. De Clercq, K. Deroover, G. Flouris, D. Lontkovskyi, S. Lowette, I. Marchesini, S. Moortgat, L. Moreels, Q. Python, K. Skovpen, S. Tavernier, W. Van Doninck, P. Van Mulders, I. Van Parijs
Universit´e Libre de Bruxelles, Bruxelles, Belgium
D. Beghin, B. Bilin, H. Brun, B. Clerbaux, G. De Lentdecker, H. Delannoy, B. Dorney, G. Fasanella, L. Favart, R. Goldouzian, A. Grebenyuk, A.K. Kalsi, T. Lenzi, J. Luetic, N. Postiau, E. Starling, L. Thomas, C. Vander Velde, P. Vanlaer, D. Vannerom, Q. Wang
Ghent University, Ghent, Belgium
T. Cornelis, D. Dobur, A. Fagot, M. Gul, I. Khvastunov2, D. Poyraz, C. Roskas, D. Trocino,
M. Tytgat, W. Verbeke, B. Vermassen, M. Vit, N. Zaganidis
Universit´e Catholique de Louvain, Louvain-la-Neuve, Belgium
H. Bakhshiansohi, O. Bondu, S. Brochet, G. Bruno, C. Caputo, P. David, C. Delaere, M. Delcourt, B. Francois, A. Giammanco, G. Krintiras, V. Lemaitre, A. Magitteri, A. Mertens, M. Musich, K. Piotrzkowski, A. Saggio, M. Vidal Marono, S. Wertz, J. Zobec
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
F.L. Alves, G.A. Alves, M. Correa Martins Junior, G. Correia Silva, C. Hensel, A. Moraes, M.E. Pol, P. Rebello Teles
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
E. Belchior Batista Das Chagas, W. Carvalho, J. Chinellato3, E. Coelho, E.M. Da Costa,
G.G. Da Silveira4, D. De Jesus Damiao, C. De Oliveira Martins, S. Fonseca De Souza,
H. Malbouisson, D. Matos Figueiredo, M. Melo De Almeida, C. Mora Herrera, L. Mundim, H. Nogima, W.L. Prado Da Silva, L.J. Sanchez Rosas, A. Santoro, A. Sznajder, M. Thiel,
E.J. Tonelli Manganote3, F. Torres Da Silva De Araujo, A. Vilela Pereira
Universidade Estadual Paulistaa, Universidade Federal do ABCb, S˜ao Paulo, Brazil
S. Ahujaa, C.A. Bernardesa, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M. Gregoresb,
P.G. Mercadanteb, S.F. Novaesa, SandraS. Padulaa, D. Romero Abadb
Bulgaria
A. Aleksandrov, R. Hadjiiska, P. Iaydjiev, A. Marinov, M. Misheva, M. Rodozov, M. Shopova, G. Sultanov
University of Sofia, Sofia, Bulgaria
A. Dimitrov, L. Litov, B. Pavlov, P. Petkov
Beihang University, Beijing, China
W. Fang5, X. Gao5, L. Yuan
Institute of High Energy Physics, Beijing, China
M. Ahmad, J.G. Bian, G.M. Chen, H.S. Chen, M. Chen, Y. Chen, C.H. Jiang, D. Leggat, H. Liao,
Z. Liu, F. Romeo, S.M. Shaheen6, A. Spiezia, J. Tao, C. Wang, Z. Wang, E. Yazgan, H. Zhang,
J. Zhao
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
Y. Ban, G. Chen, A. Levin, J. Li, L. Li, Q. Li, Y. Mao, S.J. Qian, D. Wang, Z. Xu
Tsinghua University, Beijing, China
Y. Wang
Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C.A. Carrillo Montoya, L.F. Chaparro Sierra, C. Florez,
C.F. Gonz´alez Hern´andez, M.A. Segura Delgado
University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
B. Courbon, N. Godinovic, D. Lelas, I. Puljak, T. Sculac
University of Split, Faculty of Science, Split, Croatia
Z. Antunovic, M. Kovac
Institute Rudjer Boskovic, Zagreb, Croatia
V. Brigljevic, D. Ferencek, K. Kadija, B. Mesic, A. Starodumov7, T. Susa
University of Cyprus, Nicosia, Cyprus
M.W. Ather, A. Attikis, M. Kolosova, G. Mavromanolakis, J. Mousa, C. Nicolaou, F. Ptochos, P.A. Razis, H. Rykaczewski
Charles University, Prague, Czech Republic
M. Finger8, M. Finger Jr.8
Escuela Politecnica Nacional, Quito, Ecuador
E. Ayala
Universidad San Francisco de Quito, Quito, Ecuador
E. Carrera Jarrin
Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
A. Ellithi Kamel9, M.A. Mahmoud10,11, E. Salama11,12
National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
S. Bhowmik, A. Carvalho Antunes De Oliveira, R.K. Dewanjee, K. Ehataht, M. Kadastik, M. Raidal, C. Veelken
Department of Physics, University of Helsinki, Helsinki, Finland
P. Eerola, H. Kirschenmann, J. Pekkanen, M. Voutilainen
Helsinki Institute of Physics, Helsinki, Finland
J. Havukainen, J.K. Heikkil¨a, T. J¨arvinen, V. Karim¨aki, R. Kinnunen, T. Lamp´en, K. Lassila-Perini, S. Laurila, S. Lehti, T. Lind´en, P. Luukka, T. M¨aenp¨a¨a, H. Siikonen, E. Tuominen, J. Tuominiemi
Lappeenranta University of Technology, Lappeenranta, Finland
T. Tuuva
IRFU, CEA, Universit´e Paris-Saclay, Gif-sur-Yvette, France
M. Besancon, F. Couderc, M. Dejardin, D. Denegri, J.L. Faure, F. Ferri, S. Ganjour, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry, C. Leloup, E. Locci, J. Malcles, G. Negro, J. Rander,
A. Rosowsky, M. ¨O. Sahin, M. Titov
Laboratoire Leprince-Ringuet, Ecole polytechnique, CNRS/IN2P3, Universit´e Paris-Saclay, Palaiseau, France
A. Abdulsalam13, C. Amendola, I. Antropov, F. Beaudette, P. Busson, C. Charlot,
R. Granier de Cassagnac, I. Kucher, A. Lobanov, J. Martin Blanco, M. Nguyen, C. Ochando, G. Ortona, P. Paganini, P. Pigard, R. Salerno, J.B. Sauvan, Y. Sirois, A.G. Stahl Leiton, A. Zabi, A. Zghiche
Universit´e de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
J.-L. Agram14, J. Andrea, D. Bloch, J.-M. Brom, E.C. Chabert, V. Cherepanov, C. Collard,
E. Conte14, J.-C. Fontaine14, D. Gel´e, U. Goerlach, M. Jansov´a, A.-C. Le Bihan, N. Tonon,
P. Van Hove
Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne, France
S. Gadrat
Universit´e de Lyon, Universit´e Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique Nucl´eaire de Lyon, Villeurbanne, France
S. Beauceron, C. Bernet, G. Boudoul, N. Chanon, R. Chierici, D. Contardo, P. Depasse, H. El Mamouni, J. Fay, L. Finco, S. Gascon, M. Gouzevitch, G. Grenier, B. Ille, F. Lagarde,
I.B. Laktineh, H. Lattaud, M. Lethuillier, L. Mirabito, A.L. Pequegnot, S. Perries, A. Popov15,
V. Sordini, M. Vander Donckt, S. Viret, S. Zhang
Georgian Technical University, Tbilisi, Georgia
T. Toriashvili16
Tbilisi State University, Tbilisi, Georgia
I. Bagaturia17
RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
C. Autermann, L. Feld, M.K. Kiesel, K. Klein, M. Lipinski, M. Preuten, M.P. Rauch,
C. Schomakers, J. Schulz, M. Teroerde, B. Wittmer, V. Zhukov15
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
A. Albert, D. Duchardt, M. Endres, M. Erdmann, T. Esch, R. Fischer, S. Ghosh, A. G ¨uth, T. Hebbeker, C. Heidemann, K. Hoepfner, H. Keller, S. Knutzen, L. Mastrolorenzo, M. Merschmeyer, A. Meyer, P. Millet, S. Mukherjee, T. Pook, M. Radziej, H. Reithler, M. Rieger, F. Scheuch, A. Schmidt, D. Teyssier
RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
G. Fl ¨ugge, O. Hlushchenko, T. Kress, A. K ¨unsken, T. M ¨uller, A. Nehrkorn, A. Nowack,
C. Pistone, O. Pooth, D. Roy, H. Sert, A. Stahl18
Deutsches Elektronen-Synchrotron, Hamburg, Germany
M. Aldaya Martin, T. Arndt, C. Asawatangtrakuldee, I. Babounikau, K. Beernaert, O. Behnke,
U. Behrens, A. Berm ´udez Mart´ınez, D. Bertsche, A.A. Bin Anuar, K. Borras19, V. Botta,
A. Campbell, P. Connor, C. Contreras-Campana, F. Costanza, V. Danilov, A. De Wit, M.M. Defranchis, C. Diez Pardos, D. Dom´ınguez Damiani, G. Eckerlin, T. Eichhorn, A. Elwood,
E. Eren, E. Gallo20, A. Geiser, J.M. Grados Luyando, A. Grohsjean, P. Gunnellini, M. Guthoff,
M. Haranko, A. Harb, J. Hauk, H. Jung, M. Kasemann, J. Keaveney, C. Kleinwort, J. Knolle,
D. Kr ¨ucker, W. Lange, A. Lelek, T. Lenz, K. Lipka, W. Lohmann21, R. Mankel, I.-A.
Melzer-Pellmann, A.B. Meyer, M. Meyer, M. Missiroli, G. Mittag, J. Mnich, V. Myronenko, S.K. Pflitsch, D. Pitzl, A. Raspereza, M. Savitskyi, P. Saxena, P. Sch ¨utze, C. Schwanenberger, R. Shevchenko, A. Singh, H. Tholen, O. Turkot, A. Vagnerini, G.P. Van Onsem, R. Walsh, Y. Wen, K. Wichmann, C. Wissing, O. Zenaiev
University of Hamburg, Hamburg, Germany
R. Aggleton, S. Bein, L. Benato, A. Benecke, V. Blobel, M. Centis Vignali, T. Dreyer, E. Garutti, D. Gonzalez, J. Haller, A. Hinzmann, A. Karavdina, G. Kasieczka, R. Klanner, R. Kogler, N. Kovalchuk, S. Kurz, V. Kutzner, J. Lange, D. Marconi, J. Multhaup, M. Niedziela, D. Nowatschin, A. Perieanu, A. Reimers, O. Rieger, C. Scharf, P. Schleper, S. Schumann, J. Schwandt, J. Sonneveld, H. Stadie, G. Steinbr ¨uck, F.M. Stober, M. St ¨over, D. Troendle, A. Vanhoefer, B. Vormwald
Karlsruher Institut fuer Technology
M. Akbiyik, C. Barth, M. Baselga, S. Baur, E. Butz, R. Caspart, T. Chwalek, F. Colombo, W. De Boer, A. Dierlamm, K. El Morabit, N. Faltermann, B. Freund, M. Giffels,
M.A. Harrendorf, F. Hartmann18, S.M. Heindl, U. Husemann, F. Kassel18, I. Katkov15,
S. Kudella, H. Mildner, S. Mitra, M.U. Mozer, Th. M ¨uller, M. Plagge, G. Quast, K. Rabbertz, M. Schr ¨oder, I. Shvetsov, G. Sieber, H.J. Simonis, R. Ulrich, S. Wayand, M. Weber, T. Weiler, S. Williamson, C. W ¨ohrmann, R. Wolf
Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
G. Anagnostou, G. Daskalakis, T. Geralis, A. Kyriakis, D. Loukas, G. Paspalaki, I. Topsis-Giotis
National and Kapodistrian University of Athens, Athens, Greece
G. Karathanasis, S. Kesisoglou, P. Kontaxakis, A. Panagiotou, I. Papavergou, N. Saoulidou, E. Tziaferi, K. Vellidis
National Technical University of Athens, Athens, Greece
K. Kousouris, I. Papakrivopoulos, G. Tsipolitis
University of Io´annina, Io´annina, Greece
I. Evangelou, C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, S. Mallios, N. Manthos, I. Papadopoulos, E. Paradas, J. Strologas, F.A. Triantis, D. Tsitsonis
MTA-ELTE Lend ¨ulet CMS Particle and Nuclear Physics Group, E ¨otv ¨os Lor´and University, Budapest, Hungary
M. Bart ´ok22, M. Csanad, N. Filipovic, P. Major, M.I. Nagy, G. Pasztor, O. Sur´anyi, G.I. Veres
![Table 2: Phase space definitions for cross section measurements at 8 TeV [6] and 13 TeV [8]](https://thumb-eu.123doks.com/thumbv2/123dok_br/15725680.1070954/10.892.250.648.283.448/table-phase-space-definitions-cross-section-measurements-tev.webp)
